For　nonlinear　space-varying　parabolic　partial　differential　equation　systems　(PPDESs)　with　random　time-varying　delay,　this　paper　introduces　a　dynamic　fuzzy　boundary　output　feedback　(DFBOF)　control　under　non-collocated　boundary　measurement　(NCBM).　Initially,　the　nonlinear　delayed　PPDESs　are　represented　by　Takagi-Sugeno　(T–S)　fuzzy　models　and　random　time-varying　delay　is　considered　by　taking　the　influence　of　uncertain　factors,　which　belongs　to　two　intervals　in　a　probabilistic　way.　Since　the　system　state　is　not　fully　available　and　NCBM　makes　the　boundary　control　design　very　difficult,　a　fuzzy　observer　under　NCBM　is　presented　to　surmount　the　design　difficulty.　Subsequently,　an　observer-based　fuzzy　boundary　controller　is　proposed　and　spatial　linear　matrix　inequality　(SLMI)　based　sufficient　conditions　to　ensure　mean　square　exponential　stability　are　obtained　for　closed-loop　delayed　PPDESs　by　utilizing　the　Lyapunov　direct　method　and　Wirtinger　inequality.　Then,　to　solve　the　SLMIs,　the　feasibility　conditions　of　DFBOF　controller　design　for　nonlinear　delayed　PPDES　are　expressed　in　LMIs.　Lastly,　two　examples　are　offered　to　demonstrate　the　validity　of　the　presented　dynamic　fuzzy　boundary　control　approach.　IEEE